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Simplifying w2 + 10w = 120 Reorder the terms: 10w + w2 = 120 Solving 10w + w2 = 120 Solving for variable 'w'. Reorder the terms: -120 + 10w + w2 = 120 + -120 Combine like terms: 120 + -120 = 0 -120 + 10w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '120' to each side of the equation. -120 + 10w + 120 + w2 = 0 + 120 Reorder the terms: -120 + 120 + 10w + w2 = 0 + 120 Combine like terms: -120 + 120 = 0 0 + 10w + w2 = 0 + 120 10w + w2 = 0 + 120 Combine like terms: 0 + 120 = 120 10w + w2 = 120 The w term is 10w. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10w + 25 + w2 = 120 + 25 Reorder the terms: 25 + 10w + w2 = 120 + 25 Combine like terms: 120 + 25 = 145 25 + 10w + w2 = 145 Factor a perfect square on the left side: (w + 5)(w + 5) = 145 Calculate the square root of the right side: 12.041594579 Break this problem into two subproblems by setting (w + 5) equal to 12.041594579 and -12.041594579.Subproblem 1
w + 5 = 12.041594579 Simplifying w + 5 = 12.041594579 Reorder the terms: 5 + w = 12.041594579 Solving 5 + w = 12.041594579 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + w = 12.041594579 + -5 Combine like terms: 5 + -5 = 0 0 + w = 12.041594579 + -5 w = 12.041594579 + -5 Combine like terms: 12.041594579 + -5 = 7.041594579 w = 7.041594579 Simplifying w = 7.041594579Subproblem 2
w + 5 = -12.041594579 Simplifying w + 5 = -12.041594579 Reorder the terms: 5 + w = -12.041594579 Solving 5 + w = -12.041594579 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + w = -12.041594579 + -5 Combine like terms: 5 + -5 = 0 0 + w = -12.041594579 + -5 w = -12.041594579 + -5 Combine like terms: -12.041594579 + -5 = -17.041594579 w = -17.041594579 Simplifying w = -17.041594579Solution
The solution to the problem is based on the solutions from the subproblems. w = {7.041594579, -17.041594579}
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